About: E6 (mathematics)

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In mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras , all of which have dimension 78; the same notation E6 is used for the corresponding root lattice, which has rank 6. The designation E6 comes from the Cartan–Killing classification of the complex simple Lie algebras (see Élie Cartan § Work). This classifies Lie algebras into four infinite series labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E6 algebra is thus one of the five exceptional cases.

Attributes	Values
rdf:type	yago:WikicatLieGroups yago:Abstraction100002137 yago:Group100031264 yago:WikicatAlgebraicGroups
rdfs:label	E6 (mathematics) (en) E6 (mathématiques) (fr) E6 (matematica) (it) E₆ (ko) E₆ (математика) (ru) E₆ (математика) (uk)
rdfs:comment	리 군론에서 E6는 다섯 개의 예외적 단순 리 군 가운데 하나다. 78차원의 리 군이며, 그 리 대수는 이다. (ko) In matematica, E6 è la sigla che contraddistingue un gruppo di Lie e la sua algebra di Lie . Il gruppo E6 è uno dei cinque eccezionali e uno dei . E6 ha rango 6 e dimensione 78. Il suo centro è il gruppo ciclico Z3. Il suo è il gruppo ciclico Z2. La sua ha 27 dimensioni (complesse) e la sua , che non è equivalente alla precedente, ha anch'essa 27 dimensioni. Nella fisica delle particelle E6 gioca un ruolo di rilievo in alcune grandi teorie unificate. (it) E6 — название некоторых групп Ли и также их алгебр Ли . E6 — одна из пяти компактных особых простых групп Ли. E6 имеет ранг 6 и размерность 78. (ru) E6 — назва виняткої групи Лі а також її алгебри Лі . E6 — одна з п'яти компактних особливих простих груп Лі. E6 має ранг 6 і розмірність 78. (uk) In mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras , all of which have dimension 78; the same notation E6 is used for the corresponding root lattice, which has rank 6. The designation E6 comes from the Cartan–Killing classification of the complex simple Lie algebras (see Élie Cartan § Work). This classifies Lie algebras into four infinite series labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E6 algebra is thus one of the five exceptional cases. (en) En mathématiques, E6 est le nom d'un groupe de Lie ; son algèbre de Lie est notée . Il s'agit de l'un des cinq groupes de Lie complexes de type exceptionnel. E6 est de rang 6 et de dimension 78. Le groupe fondamental de sa forme compacte est le groupe cyclique Z3 et son groupe d'automorphismes est le groupe cyclique Z2. Sa représentation fondamentale est de dimension complexe 27. Sa représentation duale est également de dimension 27. En physique des particules, E6 joue un rôle dans certaines théories de grande unification. (fr)
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dcterms:subject	Exceptional Lie algebras Algebraic groups Lie groups
Wikipage page ID	293725 (xsd:integer)
Wikipage revision ID	1040335753 (xsd:integer)
Link from a Wikipage to another Wikipage	En (Lie algebra) Algebraic group Jordan algebra Vector space Dynkin diagram Exceptional Lie algebras E6 polytope E7 (mathematics) Index of a subgroup Lie group Algebraic groups Compact space Mathematics SO(10) (physics) Chevalley basis Octonionic projective plane Simple group Gauge symmetry Grand unification theory Grand unified theory Convex hull Root lattice Lie algebra Standard model Complex dimension Freudenthal magic square Fundamental representation Particle physics Symmetry group Automorphism Dual representation G2 (mathematics) Galois cohomology Linear span Schur multiplier Lie groups Cyclic group E8 (mathematics) Exceptional simple Lie group Finite field Outer automorphism group Dimensional reduction Isometry group Riemannian manifold Coxeter group ADE classification Albert algebra Supergravity Symmetry breaking 27 lines on a cubic surface Classification of finite simple groups Group of Lie type Rosenfeld projective plane Octonion Cartan subalgebra Singlet state University of Chicago Press F4 (mathematics) Simple Lie algebra Weyl character formula Perfect field Weyl group Lang–Steinberg theorem Gauge group Rank of a Lie group Simple root (root system) Weyl spinor

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